All atomic nuclei of elements with an odd atomic mass or an odd atomic number possess a nuclear magnetic moment. Nuclear magnetic resonance is a phenomenon exhibited by this select group of atomic nuclei (termed "NMR active" nuclei), and is based upon the interaction of the nucleus with an applied, external magnetic field. The magnetic properties of a nucleus are conveniently discussed in terms of two quantities: the gyromagnetic ratio (.gamma.); and the nuclear spin (I). When an NMR active nucleus is placed in a magnetic field, its nuclear magnetic energy levels are split in to (2I+1) non-degenerate energy levels, which are separated from each other by an energy difference that is directly proportional to the strength of the applied magnetic field. This splitting is called the "Zeeman" splitting and the energy difference is equal to .gamma.hH.sub.0 /2.pi., where h is Plank's constant and H.sub.0 is the strength of the applied magnetic field. The frequency corresponding to the energy of the Zeeman splitting (.omega..sub.0 =.gamma.H.sub.0) is called the "Larmor frequency" and is proportional to the field strength of the magnetic field. Typical NMR active nuclei include .sup.1 H (protons), .sup.13 C, .sup.19 F, and .sup.31 P. For these four nuclei I=1/2, and each nucleus has two nuclear magnetic energy levels.
When a bulk sample of material containing NMR active nuclei is placed within a magnetic field called the main static field, the nuclear spins distribute themselves amongst the nuclear magnetic energy levels in accordance with Boltzmann's statistics. This results in a population imbalance among the energy levels and a net nuclear magnetization. It is this net nuclear magnetization that is studied by NMR techniques.
At equilibrium, the net nuclear magnetization of the aforementioned bulk sample is aligned parallel to the external magnetic field and is static (by convention, the direction of the main static field is taken to be the Z-axis). A second magnetic field perpendicular to the main static magnetic field and rotating at, or near, the Larmor frequency can be applied to induce a coherent motion of the net nuclear magnetization. Since, at conventional main static magnetic field strengths, the Larmor frequency is in the megahertz frequency range, this second magnetic field is called a "radio frequency" or RF field.
The effect of the RF field is to shift the nuclear magnetization direction so that it is no longer parallel to the main static field. This shift introduces a net coherent motion of the nuclear magnetization about the main static field direction called a "nutation". In order to conveniently deal with this nutation, a reference frame is used which rotates about the laboratory reference frame Z-axis at the Larmor frequency and also has its Z-axis parallel to the main static field direction. In this "rotating frame" the net nuclear magnetization, which is rotating in the stationary "laboratory" reference frame, is now static.
Consequently, the effect of the RF field is to rotate the now static nuclear magnetization direction at an angle with respect to the main static field direction (Z-axis). The new magnetization direction can be broken into a component which is parallel to the main field direction (Z-axis direction) and a component which lies in the plane transverse to the main magnetization (X-Y plane). The RF field is typically applied in pulses of varying length and amplitude and, by convention, an RF pulse of sufficient amplitude and length to rotate the nuclear magnetization in the rotating frame through an angle of 90.degree., or .pi./2 radians, and entirely into the X-Y plane is called a ".pi./2 pulse".
Because the net nuclear magnetization is rotating with respect to the laboratory frame, the component of the nuclear magnetization that is transverse to the main magnetic field or that lies in the X-Y plane rotates about the external magnetic field at the Larmor frequency. This rotation can be detected with a receiver coil that is resonant at the Larmor frequency. The receiver coil is generally located so that it senses voltage changes along one axis (for example, the X-axis) where the rotating magnetization component appears as an oscillating voltage. Frequently, the "transmitter coil" employed for applying the RF field to the sample and the "receiver coil" employed for detecting the magnetization are one and the same coil.
Although the main static field is applied to the overall material sample, the nuclear magnetic moment in each nucleus within the sample actually experiences an external magnetic field that is changed from the main static field value due to a screening from the surrounding electron cloud. This screening results in a slight shift in the Larmor frequency for that nucleus (called the "chemical shift" since the size and symmetry of the shielding effect is dependent on the chemical composition of the sample).
In a typical NMR experiment, the sample is placed in the main static field and a .pi./2 pulse is applied to shift the net magnetization into the transverse plane (called transverse magnetization). After application of the pulse, the transverse magnetization, or "coherence", begins to precess about the Z-axis, or evolve, due to the chemical shifts at a frequency which is proportional to the chemical shift field strength. In the rotating frame, the detector (which is stationary in the laboratory frame) appears to rotate at the Larmor frequency. Consequently, the detector senses an oscillation produced by an apparent magnetization rotation at a frequency which is proportional to the frequency difference between the Larmor frequency and the chemical shift frequency.
Thus, the detected signal oscillates at the frequency shift difference. In addition to precessing at the Larmor frequency, in the absence of the applied RF field energy, the nuclear magnetization also undergoes two spontaneous processes: (1) the precessions of various individual nuclear spins which generate the net nuclear magnetization become dephased with respect to each other so that the magnetization within the transverse plane loses phase coherence (so-called "spin-spin relaxation") with an associated relaxation time, T.sub.2, and (2) the individual nuclear spins return to their equilibrium population of the nuclear magnetic energy levels (so-called "spin-lattice relaxation") with an associated relaxation time, T.sub.1. The latter process causes the received signal to decay to zero. The decaying, oscillating signal is called a free induction decay (FID).
In a typical NMR experiment, the FID is repeatedly sampled at discrete time intervals and the corresponding amplitude digitized. The resulting digital samples are generally subjected to a Fourier transformation which produces a frequency spectrum having peaks at the chemical shift frequencies. This type of NMR experiment is called a one-dimensional NMR experiment.
It is often useful to exploit the coupling of one nucleus to another to explore spin coherences between nuclei. One extremely powerful application of such coherence transformations is found in multi-dimensional experiments. In such experiments, the spins are excited and spin evolution proceeds for an evolution time. The spins are then driven through a coherence transformation by a mixing pulse and, finally, the evolution is detected. A two-dimensional Fourier tansformation then yields a correlation of the spin states prior to, and following, the mixing pulse.
An important strength of modern NMR spectroscopy is the ability to drive the dynamics of the spin system through a series of coherence transformations such that the resultant observable magnetization reflects desired combinations of evolutions and interactions. Coherence transformations can be used not only for transferring magnetization from one spin to another (such as described in detail below), but also for "filtering" purposes to select only those spin systems with a given property (such as in multiple-quantum filters).
For example, coherence transformations can be used in a two-dimensional (2D) NMR experiment to display correlations between coupled spins. A typical 2D experiment involves the interaction of each .sup.1 H nucleus (proton) with all of its coupling partners. In the experiment, the protons are excited during a "preparation" time period by an application of a .pi./2 RF pulse at the proton resonant frequency. The resulting coherence evolves under influence of the chemical shift during an "evolution" time period. The coherence is transferred between coupled protons during a "mixing" period by applying a second RF pulse to the protons (this process is sometimes called "polarization transfer"). Finally, during a detection period, the FID is sampled and collected.
The resulting FID signal is modulated not only by the chemical shift evolution of the protons during the detection period but also by the evolution period spin evolution of coupled protons. Since, the resulting signal depends on the correlation of two nuclei, the process is often called COrrelation SpectroscopY (COSY).
The resulting FID signal is processed in a manner similar to the one-dimensional experiment by taking the Fourier transformation of the signal. However, a second time dimension is introduced by repeating the experiment while systematically varying the length of the evolution time period. The resulting set of FIDs are then subject to a second Fourier transformation over the varying time of the evolution period. The two frequency spectra can be plotted along the horizontal and vertical coordinates of a graph to produce a two-dimensional plot. This plot has "peaks" which represent coherence transformations and, therefore, is useful in studying molecular structure.
As described in the 2D NMR example above, coherence transformations are most often accomplished via RF pulses. The fine selectivity desired is rarely achieved by a single sequence of RF pulses and is most often built up over a series of separate experiments, each of which uses a sequence of RF pulses. The phases of selected RF pulses in each sequence are often modulated, or cycled, from experiment to experiment while all other variables are kept constant. In these latter experiments, the phase of the observation (the receiver phase) is also modulated along with the pulse phase. The results of several experiments are then averaged to generate an overall result. In this manner, selected magnetization that is modulated in the same way as the receiver phase is modulated is retained in the overall result while other unwanted magnetization is eventually averaged to zero.
For example, in the 2D NMR example discussed above, the selectivity produced by the mixing pulses is degraded by several problems. One problem is so-called "axial" peaks that are generated by magnetization which did not evolve under influence of the proton chemical shift during the evolution period (such as magnetization excited by the mixing pulse). Another problem is that the resulting 2D spectrum appears as a mirror image of itself (the two sets of peaks are called n-type" peaks and "p-type" peaks) since the experiment cannot distinguish the sense (right or left) of the magnetization rotation during the evolution period. Other problems include instrument artifacts and noise. The axial pulses, mirrored peaks, artifacts and noise can obscure signal data in complicated spectra and make interpretation of the data difficult.
These problems are generally dealt with by phase cycling the mixing pulse in the COSY sequence. By properly phase cycling the mixing pulse and adding the results of several experiments, the axial pulses and some artifacts can be eliminated and one set of pulses (the n-type or the p-type) can be selected.
Phase cycling is a widely used and very powerful concept, but, in some cases, phase cycling leads to an inefficient use of spectrometer time because multiple experiments must be run. In addition, phase cycling is susceptible to additional artifacts arising from spectrometer instabilities and from non-steady state conditions which changes the starting magnetization between experiments.
Consequently, the prior art has sought a method for improving the selectivity of coherence transformations without requiring that the results of multiple experiments be averaged. One prior art method is a single FID acquisition alternative to phase cycling that uses magnetic gradient pulses to improve selectivity. These gradient pulses superimpose a spatially dependent magnetic field on the main static field (B.sub.0) and suppress unwanted coherence transformations. For example, in the 2D COSY experiment described above, gradient pulses can be applied both before and after the mixing pulse to suppress axial pulses and select either n-type or p-type peaks.
Another prior art approach is to use RF (B.sub.1) magnetic gradients superimposed on the RF pulses (which are normally homogeneous over the sample) to improve selectivity. This latter technique has been investigated, but not widely used.
Accordingly, it is an object of the present invention to improve the selectivity of coherence transformations without incurring the time and accuracy penalties of the phase cycling method.